Question

write the expression in simplest form:- sec^2-1/cosec^2-1​

Answer 1

Answer:

identity: 1 + tan square theta= sec squre theta

and 1+ cot square theta = cosec square theta

replace that in question you get tan square theta / cot square theta

but tan theta is sin theta / cos theta and cot theta is cos theta / sin theta therefore final answer is sin theta to the power 4/ cos theta to the power 4

Answer 2

Answer:

= sec²-1/cosec²-1

= tan²/cot². (tan² = sec²-1. & cot² = cosec²-1)

= (sin²/cos²) / (cos²/sin²)

(tan²=sin²/cos² & cot²=cos²/sin²)

= sin² x sin²/cos² x cos²

=sin⁴/cos⁴...Answer